Policy Optimization Over Submanifolds for Linearly Constrained Feedback Synthesis

• 成果类型: Article
• 署名作者: Talebi, Shahriar; Mesbahi, Mehran
• 署名单位: University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3306384
• 发表日期: 2024
• 页码: 3024-3039
• 关键词: Optimization over submanifolds; output-feedback linear quadratic regulator (LQR) control; structured LQR (SLQR) control; constrained stabilizing controllers

摘要

In this article, we study linearly constrained policy optimization over the manifold of Schur stabilizing controllers, equipped with a Riemannian metric that emerges naturally in the context of optimal control problems. We provide extrinsic analysis of a generic constrained smooth cost function that subsequently facilitates subsuming any such constrained problem into this framework. By studying the second-order geometry of this manifold, we provide a Newton-type algorithm that does not rely on the exponential mapping nor a retraction, while ensuring local convergence guarantees. The algorithm hinges instead upon the developed stability certificate and the linear structure of the constraints. We then apply our methodology to two well-known constrained optimal control problems. Finally, several numerical examples showcase the performance of the proposed algorithm.